Solve the problem.

Question

If a model rocket is propelled upward from ground level at an initial velocity of 112 feet per second, after t seconds, its height h is given by the formula h=-16t²+112t. After how many seconds will its height be 160 feet?

Answer 1

Set h(t) = 160 and solve for t:

 

160 = -16t² + 112t

16t² - 112t + 160 = 0

 

Divide both sides by 16:

 

t² - 7t + 10 = 0

(t-2)(t-5) = 0

 

t = 2 and 5 seconds

 

The rocket will reach 160 feet at t=2 seconds on its way up, and again at t = 5 seconds on its way back down.